Is There New Physis Around the Corner?
O. J.P.
Eboli
InstitutodeFsiaTeoria,
UniversidadeEstadual Paulista
Rua Pamplona145,S~aoPaulo,SP01405{900,Brazil
E-mail: eboliift.unesp.br
Reeived7January,2000
TherearemanytheoretialargumentsindiatingthatthereshouldbenewPhysisaroundtheTeV
sale whihanbedisoveredinthenextdeade. Webrieyreviewsomeofthepossiblesenarios
whihgiverisetoaplethoraofnewsignalsatolliderexperiments.
I New Physis Senarios
In the last few years it hasbeen established that the
interationsof thegaugebosonswith thefermionsare
well desribedby theStandardModel(SM) [1℄.
How-ever,wehavenotobservedtheSU(2)
L U(1)
Y
symme-trybreakingmehanismyet. Atpresent,thebest
avail-able limiton the SM Higgs mass arises from searhes
at the CERN LEP ollider. The ALEPH
Collabora-tionanalysisofthe1999datawithintegrated
luminosi-tiesof 29 pb 1
at p
s =191:6 GeV and 69.5pb 1
at
p
s=195:6GeV[2℄yieldsM
H
>98:8GeVat95%CL.
The preision measurements performed at the Z
peak exhibit an agreement at the per mile level with
theSMtheoretialpreditions[1℄. Suhapreision
al-lows us to obtain information on the Higgs boson via
loopeetsdespiteitsontributionbeingonly
logarith-mi upon the Higgs mass. Performing a global t to
theavailable datawithin theframeworkof theSM
al-low us to onstraints the Higgs mass [3℄; see Fig. 1.
At the 95% CL the SM Higgs mass is bounded from
aboveM
H
<230GeV.Therefore,weshouldbeableto
startprobingthesymmetrybreakingmehanisminthe
nextfew years at theTevatron orthe LHC if theSM
desribesorretlythismehanism.
Howeverthis might be not the whole story! The
analysis of the stability of the SM vauum implies
that the quarti Higgs oupling is bounded from
be-low, whih orresponds to a lower limit on the Higgs
mass [4℄. Requiring that theSM vauum is stable up
totheGUTsale(10 16
GeV),wemusthaveM
H >130
GeV.Moreover,the runningquarti Higgs ouplingis
givenby
1
() =
1
(M
H )
3
4 2
log
2
M 2
H
; (1)
nite sale. This pole signalsthe appearane of new
physis. Again,assumingtheSMtobevalidupto the
GUTsaleleadstoM
H
<180GeV[5℄.
0
2
4
6
10
10
2
10
3
m
H
[GeV]
∆χ
2
Excluded
Preliminary
∆α
had
=
∆α
(5)
0.02804
±
0.00065
0.02784±0.00026
theory uncertainty
Figure1. 2
oftheSMglobaltasafuntionoftheHiggs
mass.
Fromtheabovedisussion, theSMwithone Higgs
doubletmightdesribethewholepartilephysisupto
theGUT saleprovided130<M
H
<180GeV.
How-ever,eveniftheHiggsisdisoveredin thismassrange
it is unlikely that the SM is the whole truth sine it
is unnatural to have alight salar in a model with a
meha-heavysaledue to radiativeorretions. Onesolution
tothenaturalnessproblemistointrodue
supersymme-try(SUSY)attheTeVsale. Inthisase,thereshould
be plenty of new partiles waiting to be found in the
nextfewyears.
Another distint possibility is that the symmetry
breaking mehanism does not exhibit a Higgs boson.
This happens in models with dynamial symmetry
breaking. Here, theoretial argumentsalso point that
the new physis sale is low enough to be tested in
thenextgenerationof olliders. Infat,thesattering
WW !WW violatesunitarityforenergieslargerthan
4v ' 3TeV if there is no Higgs boson [6℄. This
in-diates that weshould have newstates at this energy
sale orthat thetheory beomes stronglyinterating.
Againtherewillbeplentyofexitementwhenwestart
to probetheTeVsaleifthisistheorretsenario!
Reentlytherehasbeenagreatinterestinthe
pos-sibilitythatthesaleofquantumgravityisoftheorder
of theeletroweaksale [7℄insteadofthePlanksale
M
pl ' 10
19
GeV. The known onstrutions of a
on-sistent quantum gravity theory require the existene
of extra dimensions [8℄, whih should have been
om-patied. AsimpleargumentbasedontheGauss'law
in arbitrarydimensionsshowsthatthe Planksaleis
related to theradius of ompatiation (R ) of the n
extradimensionsandthequantumgravitysaleby
M 2
pl 'R
n
M n+2
S
; (2)
where M
S
is the (4 + n) dimensional fundamental
Planksaleorthestringsale. Thusthe largenessof
the4 dimensionalPlanksaleM
pl
(orsmallnessofthe
Newton's onstant)an be attributed to theexistene
of largeextradimensionsofvolume R n
. If one
identi-esM
S
O(1 TeV),thissenarioresolvestheoriginal
gauge hierarhy problem between the weak sale and
thefundamental Planksale,andleadtorih low
en-ergy phenomenology. The n = 1 ase orresponds to
R'10 8
km,whihisruledoutbyobservationon
plan-etarymotion. Intheaseoftwoextradimensions,the
gravitationalfore ismodied onthe 0:1 mm sale; a
region notsubjettodiret experimentalsearhesyet.
However, astrophysisonstraintsfrom supernovahas
set alimitM
S
>30TeVforn=2[9℄,andthus
disfa-vored asasolutionto thegaugehierarhyproblem as
wellasforadiret ollidersearh.
Generallyspeaking, whentheextradimensionsget
ompatied, the elds propagating there give riseto
towers of Kaluza-Klein states [10℄, separated in mass
by O(1=R ). Inorderto evadestrongonstraintsfrom
eletroweak preisionmeasurementsthe SM elds are
assumed to liveon a4{dimensionalhypersurfae,and
only gravitypropagatesin theextradimensions. This
assumption is basedon newideasaboutthe D-branes
[11℄. If gravity beomes strong at the TeV sale,
Kaluza{Klein (KK) gravitons should play a r^ole in
asavirtualexhangestate. Therehasbeenmuhwork
in the reent literature to explore the ollider
onse-quenesfortheKK gravitons[12,13℄.
The above new physis senariosare just a
repre-sentativesetofthelargenumberofpossibleextensions
of the SM. Inthe followingwedesribesome of their
phenomenologialimpliations and the respetive
sig-nalsat olliders. Our main pointis that thesemodels
giverisetosuhalargenumberofnewtopologiesthat
theirstudy will over almost all newphysis
possibil-ities, even the ones not onsidered here, guaranteeing
thattheexperimentswillnotmissanynewphysissign
intheTeVsale!
II Higgs Searhes
NowadaysLEPIIisthemahinewiththelargest
apa-bilitytostudytheprodutionofHiggsbosonsprovided
M
H
isnottoolarge. AtLEPenergiesthemainHiggs
produtionmehanismis[14℄
e +
e !ZH ; (3)
whosetotalrosssetionwepresentinFig. 2.This
pro-essallowus to probeHiggs masses up to ' p
s 95
GeV[14℄.
Figure2. SMHiggs prodution rosssetion at LEP as a
funtionofM
H
fordierententer{of{massenergies[14 ℄.
TheSMHiggssignaldependsonitspossibledeays
whih are displayin Fig. 3. Taking into aount the
Z andHiggsdeayhannels,theSMHiggsprodution
topologiesaretheonesshowninTable1. Animportant
featureoftheseHiggstopologiesisthepreseneofjets
taggedasb-jets sinealightHiggshasalarge
theHiggs searh aretheW +
W andZZ produtions
whose ross setions are roughly 20 and 1 pb
respe-tively. An eÆientwayto reduethebakgroundisto
require the presene of b-tagged jets in the event. In
fat,b-taggingreduesthesignalbyafator0:60while
theW +
W bakgroundisreduedbyafator0.01and
10%oftheZZ bakgroundsurvives.
Figure3. SMHiggsbranhingratiosasafuntionofthe
Higgsmass[14 ℄.
nalstate frequeny
4jets 60%
2jets+E
/
T
18%
2jets+2` 6%
2jets+2 9%
Table1. Finalstatetopologiesandexpetedfrequeniesfor
aSMHiggsbosonatLEPII.Here,`standsfore
and
.
In theLEPII experimental searhes,aneural
net-work is used to analyze the data, where many
vari-ablesare onsidered likevisible energy, missing
trans-versemomentum,invariantmassofjetpairs,displaed
verties, et. We summarize in Table 2 the 95% CL
lower limits on the SM Higgs mass obtained by the
negativeresults at 189 GeV of the four LEP
ollabo-rations, aswell as the values expeted assuming that
just the bakground has been observed [15℄. We also
presentinthistabletheombinedlimitofthefour
ol-laborations. Notie that the limits derived from data
areusuallysmallerthantheexpetedones. Thisisdue
to aslight overall exess of events whih is not
au-mulatedin asinglebin. Thisexessanoriginatefrom
statistialutuationsorsimplyasystemati
underes-InitslastyearofoperationLEPwillbeableto
ex-tend the above limitson theSM Higgs. Forinstane,
running at 198GeV with anintegrated luminosity of
200pb 1
perexperiment,itsispossibletodisoverSM
Higgs bosons with masses up to 105 GeV or to rule
outSMHiggsbosonswithmassesupto107GeV.The
next mahine that will be able to improve these
lim-its is the RUN II of the Tevatron whose performane
is summarized in Fig. 4. As weansee from this
g-ure, theTevatron anexludeHiggsmasses upto 120
GeVforanintegratedluminosityof2fb 1
. Inorderto
probethewholerangeofallowedHiggsmasseswehave
to wait until theCERN LargeHadron Collider starts
operating.
Collaboration M
H
(GeV) expeted(GeV)
ALEPH 92.9 94.1
DELPHI 94.1 94.6
L3 95.3 94.8
OPAL 91.0 94.9
Combined 95.2 97.2
Table2. LowerboundontheSMHiggsmassderivedbythe
fourLEPCollaborationsusingthedatatakenat189GeV.
For omparison we present the expeted limits assuming
that onlythebakgroundwas observed. Thelast linewas
obtainedombiningthefourexperiments.
Figure 4. Combined CDF and D integrated luminosity
neededtodisover/rule outaSMHiggsasafuntionofits
mass.
III Anomalous Higgs
Intera-tions
A veryinteresting possibility is that the new physis
manifestsitselfmodifyingtheSMHiggsprodutionand
eletroweaksale. Inthisaseweanparametrizethe
deviationsfromtheSMusingeetivelagrangianswith
alinearrepresentationoftheSU(2)
L U(1)
Y
symme-try. Asetofpossibleeetiveoperatorsis
L
e =
f
BW
2
B
y
W
+ f
2
( y
D
)(D
y
)
+ f
WW
2
W
W
y
+ f
BB
2
B
B
y
+ f
;1
2
(D
)
y
y
(D
) ; (4)
whih modify the ouplings of the Higgs to gauge
bosons. The operators O
;1
and O
BW
ontribute at
treeleveltothevetor{bosontwo{pointfuntions,and
onsequently are severely onstrained by low{energy
data [16℄. The present 95% CL limits on these
oper-ators for 90 GeV M
H
800GeV and m
top =175
GeV,read
1:2 f
;1
2
0:56TeV 2
; (5)
1:0 f
BW
2
8:6TeV 2
: (6)
Asurprising fat isthat theseresidual interations
an modify onsiderably the Higgs physis even when
we take into aount these bounds! Forinstane, we
show in Fig. 5 the allowed Higgs mass region by the
lowenergypreisiondatainludingtheeetofthe
op-eratorsO
;1 andO
BW
[17℄. Notiethedramatihange
withomparisonwithFig. 1!
Figure5. AllowedHiggsmassregionwhenweonsiderthe
eetoftheoperators O
;1 andO
BW .
The eet of the additional Higgs interations on
the properties of an intermediate mass Higgs an be
moreeasilyseeninproessesthataresuppressedinthe
SM,thisdeayoursonlyatone{looplevel,anditan
beenhaned(orsuppressed)bytheanomalous
intera-tions [18℄. Moreover, these eetive interations also
leadtonewtopologiesforHiggssearhatLEP[19℄
e +
e ! H(!) ; (7)
e +
e ! H(!b
b) : (8)
Reently theL3 analyzed these signals[20℄, obtaining
the95%CLlimitsonasafuntionoftheHiggsmass
forf
WW =f
BB
=1;seeinTable3.
M
H
70 289
90 216
110 243
130 218
Table3.95%CLlowerboundson(GeV)asafuntion
MH (GeV).
IV Supersymmetri Models
Weaksalesupersymmetrimodelsreeivedalotof
at-tention not only due to its intrinsi beauty but also
forprovidingasolutionforthenaturalness(hierarhy)
problem. Weshould notforget that these models are
perturbative and onsequently we an make reliable
preditions,ontrarytowhathappensinstrongly
inter-atingmodelsliketehniolor. Inmypointoutofview,
SUSYmodelsare aexellentframework forpreparing
theanalyses ofexperiments sinethey possess alarge
parameterspaeinitsmoregeneralformwhih,inturn,
givesrisetomanydistintpreditionsandtopologies.
In supersymmetri models the spetrum is more
thantwotimesbigger thanthe SMonesine wehave
to introdue onesupersymmetri partner foreah SM
partile and also enlargethe Higgs setor. Moreover,
sinethesupersymmetripartnersarenotdegenerated
inmasswiththeSMpartileswemustalsoadda
super-symmetrybreaking setor, and onsequently new free
parameters. Altogether thenumberof SUSY
parame-tersis largerthan100beingthis thesoureof itsrih
phenomenology.
Here,Iwill just giveabroadviewofsomepopular
SUSYsenarios. Initially wedivide the SUSYmodels
intotwolassesaordingtheyexhibitornotadisrete
symmetry alled R {parity. R {parityis related to the
partilespin(S),leptonnumber(L),andbaryon
num-ber(B)throughR=( 1)
(3B+L+2S)
, beingalltheSM
partilesR {evenwhile theirsuperpartnersareR {odd.
Neithergaugeinvarianenorsupersymmetryrequireits
onservation.
Let us start by the models with R {Parity
onser-vation. In this ase the lightest supersymmetri
pro-ConstrainedMinimalSupersymmetriStandardModel
(CMSSM)whihusessupergravitytoredue the
num-berof free parametersto 5at theGUT sale. Inthe
CMSSMitis assumedthat SUSYbreaking is
ommu-niatedtooursetorbygravitationalinterations[21℄,
resultingthatthefreeparametersareaommonSU(2)
gaugino mass (M
2
), a ommon salarmass (m
0 ), the
ratiooftheVEVofthetwoHiggsdoubletsinthemodel
(tan),theHiggsmixingparameterandtheommon
trilinearouplingA
0
. IntheCMSSM,theLSPis
neu-tral andweakinterating,therefore, itis notobserved
in detetors. The deays of the SUSY partiles lead
totheprodutionofLSP'sduetheR {parity
onserva-tion. Therefore,oneofthemainpropertiesofCMSSM
topologiesisthepreseneofsubstantialmissingenergy.
For example, theprodutionof the SUSY partners of
W
(harginos~
)anleadtothefollowingtopology
ine +
e olliders
e +
e !~ +
~
!LSPLSPW
W
; (9)
whereonlythedeayprodutoftheW
'sareobserved.
Other models exhibitingR {parityonservationare
thesoalledtheGaugeMediatedSUSYBreaking
mod-els (GMSB), where the breaking of supersymmetryis
mediatedbygaugeinterationbetweenoursetorand
the hidden setor. In this ase the harateristi
en-ergysaleanbemuhsmallerthan thePlankmass.
Thisimpliesthatthegravitinostartsplayingan
impor-tant r^ole in the phenomenology of these models sine
it is the LSP. In this ase the gravitinos are not
ob-served,alsoleadingtomissingenergysignatures.
How-ever,thesemodelsalsopossesstheadditionalproperty
thatthenexttolightestSUSYpartile(NLSP)deays
into its SM partner and a gravitino ~
G . If the NLSP
is theSUSY partner oftaus, theeventswill present a
largenumberoftausdueto ~! + ~
G. Ontheother
hand,iftheNLSP is theSUSYpartner ofthe neutral
gaugebosons~
0
,therewillbephotonrihsamplesdue
to~
0 !+
~
G. ClearlytheGMSBmodelshavea
phe-nomenologyverydistintoftheCMSSM.Forinstane
GMSB models an leadto eventspresentingtwo
pho-tonsandmissingtransverseenergyinhadroniolliders
via
pp!~
0 ~ 0 ! ~ G ~
G : (10)
We an lassify the models without R {parity
a-ordingtothemehanismofR {paritybreaking,whih
an be expliit orspontaneous. The expliit break of
R {parity takesplae byadding thefollowingtermsto
thesuperpotential ijk L i L j E k + 0 ijk L i Q j D k +00 ijk U i D j D k + i L i H u ; (11)
whih ontain thequark and leptonsuperelds Q, U,
D and L. In this senariothere are 48 extra free
pa-rameters! The SUSY phenomenologyis modied
sub-andtheLSPisnolongerstable. Moreover,SUSY
parti-lesanalsobeproduedasresonanes,leadingtonew
learsignatures. Typialbounds onthe's areof the
orderof1%exeptwhenthesenewinterationanlead
toafastprotondeay. Forinstane, 0 11k 00 11k <10 22
in thisase[22℄.
In this senario, there an be events presenting
manyjetsand/orleptons,withorwithoutmissing
en-ergy, due to omplex asade deays and to the fat
that theLSPis unstable. Forinstane,theOPAL
ol-laboration denesnine topologiesin their searhesfor
harginos[23℄,seeTable4. Notiethattherearemany
newhannelswith respet tothe CMSSMsearh that
leadstoapairofW'sandmissing energy. Sinethere
aresomanynewanddistinttopologiesinmodelswith
R {parityviolationit is possible thatwend asignof
new physis, even if it is not supersymmetri, when
looking desperatelyforSUSY!
2` +p / T 4` +p / T 6` +p / T 6` n`
+kjets 2+4jets
4jets+p
/
T
>4jets+p
/
T
6jets
Table 4. Topologiesstudiedby theOPALollaborationin
theirsearhforharginosassumingthatR {parityis
expli-itlybroken.
V Low Sale Quantum Gravity
Thephenomenologyofmodelswithlowsalequantum
gravitydierfromtheSMonesinetheyexhibittowers
of Kaluza{Kleingravitons. Despite thegraviton
inter-ation with SM partiles being suppressed by powers
of thePlankmass,they angiveriseto visible eet
sinewehavetosumuptheontributionofthewhole
graviton tower, whih trades the Plank mass by the
quantum gravity sale M
S
; see for instane [7℄.
Vir-tualgravitonexhangesmodiestheSMrosssetions
aordingto ' SM + E M S 4 ~ I + E M S 8 ~ G ; (12)
where E is aharateristienergysale oftheproess
SM , I and G
areassoiated,respetively,totheSM,
interferenegraviton{SM,and puregraviton
ontribu-tions. An interesting feature of the virtual graviton
exhange isthat it isinsensitive onthenumberof
ex-tra dimensions. Thesignature ofgravitonexhangeis
themodiationoftheenergydependene oftheross
No-with energythat iteventuallyleadsto unitarity
viola-tion. At this point, either there is the appearane of
new states to enfore unitarity or themodel beomes
stronglyinterating.
Sine graviton{matter interations are not
en-haned, gravitons esape detetion leading to missing
energy signatures. In graviton emission wemust also
sumoverallgravitonmasses
d 2
dtdm
G =
2 n=2
(n=2) M
2
P
M 2+n
S m
n 1
G
d(m
G )
dt
(13)
whihleadstoanenhanementoftherosssetion
'
E
M
S
2+n
~
: (14)
Notie thatgravitonemissiondepends stronglyonthe
numberofextradimensionsandthatiteventuallygives
risetounitarityviolation.
The presently available data from LEP and T
eva-tron onstrain the quantum gravity saleto be larger
than'1TeV[24℄. Forinstane,letusstudythelimits
thatanbeobtainedfromtheproesse +
e 
